Scripting: How to correctly group objects
I finally realised I was the one making the mistake, called a blender guru and realised grouped objects didn't move together with the keyboard shortcut so it was just the selection I used to group the objects I was misinterpreting as the group behaviour after I moved the objects together afterwards.  

After surfing the web I realised it was either the parenting property or I simply press a keyboard shortcut which brings a dropdown list to choose group and select all objects in it so I can translate at once.